When two conjugate redox pairs are present together in solution, electron transfer from the electron donor of one pair to the electron acceptor of the other may occur spontaneously. The tendency of such a reaction to occur depends upon the relative affinity of the electron acceptor of each redox pair for electrons. The standard reduction potential, Eo, a measure of this affinity, is determined in an experiment such as that described in Figure 13-15. Electrochemists have chosen as a standard of reference the half reaction H+ + e- 2H2 The electrode at which this half reaction occurs is arbitrarily assigned a standard reduction potential of 0.00 V. When this hydrogen electrode is connected through an external circuit to another half cell in which the oxidized and reduced species are both present at standard concentrations (each solute at 1 M, each gas at 1 atm), electrons will tend to flow through the external circuit from the half cell of lower standard reduction potential to the half cell of higher standard reduction potential. By convention, the half cell with the stronger tendency to acquire electrons is assigned a positive value of E0 (in volts). The reduction potential of a half cell depends not only upon the chemical species present but also upon their activities, approximated by their concentrations. About a century ago, Walther Nernst derived an equation that relates standard reduction potential (E0) to reduction potential (E) at any concentration of oxidized and reduced species in the cell: where R and T have their usual meanings (Table 13-1), n is the number of electrons transferred per molecule, and F is the Faraday constant, 96.48 kJ/V•mol. At 298 K (25 °C), this expression reduces to: Many half reactions of interest to biochemists involve protons. As in the definition of ΔG°', biochemists define the standard state for oxidation-reduction reactions as pH 7 and express reduction potential as E'0, the standard reduction potential at pH 7. The values for standard reduction potentials given in Table 13-7 and used throughout this book are for E0 and are therefore only valid for calculations involving systems at neutral pH. Each value represents the potential difference when the conjugate redox pair at 1 M concentrations at pH 7 is connected with the standard (pH 0) hydrogen electrode. Notice in Table 13-7 that when the conjugate pair 2H+/H2 at pH 7 is connected with the standard hydrogen electrode (pH 0), electrons tend to flow from the pH 7 cell to the standard (pH 0) cell; the measured ΔE'0 for the 2H+/H2 pair is -0.414 V

Figure 13-15 Measurement of the standard reduction potential (E'0) of a redox pair. Electrons flow from the test electrode to the reference electrode, or vice versa. The ultimate reference half-cell is the hydrogen electrode, as shown here. The arbitrary electromotive force (emf) of this electrode is 0.00 V. At pH 7, E'0 for the hydrogen electrode is -0.414 V. The direction of electron flow depends upon the relative electron "pressure" or potential of the two cells. A salt bridge containing a saturated KCl solution provides a path for counter-ion movement between the test cell and the reference cell. From the observed emf and the known emf of the reference cell, the emf of the test cell containing the redox pair is obtained. The cell that gains electrons has, by convention, the more positive reduction notential.

The usefulness of reduction potentials stems from the fact that when E has been determined for any two half cells, relative to the standard hydrogen electrode, their reduction potentials relative to each other are also known. One can therefore predict the direction in which electrons will tend to flow when these two half cells are connected through an external circuit, or when the components of the two half cells are present together in the same solution. Electrons will tend to flow to the half cell with the more positive E, and the strength of that tendency is proportional to the difference in reduction potentials, ΔE.

The energy made available to do work by this spontaneous electron flow (the free-energy change for the oxidation-reduction reaction) is proportional to ΔE:

ΔG=-nFΔE, or ΔG°'=-nFΔE'₀

Here n represents the number of electrons transferred in the reaction. With this equation it is possible to calculate the free-energy change for any oxidation-reduction reaction from the values of Eo (found in a table of reduction potentials) and the concentrations of the species involved in the reaction.

Consider the reaction in which acetaldehyde is reduced by the biological electron carrier NADH:

Acetaldehyde + NADH + H⁺ ethanol + NAD⁺

The relevant half reactions and their Eo values (Table 13-7) are:

(1) Acetaldehyde + 2H⁺ + 2e^- ethanol         E'₀ = -0.197 V

(2) NAD⁺ + 2H⁺ + 2e^- NADH + H⁺         E'₀ = -0.320 V

For the overall reaction, ΔE₀ = -0.197 V - (-0.320 V) = 0.123 V, and n is 2. Therefore, ΔG°' = -nFΔE'₀ = -2(96.5 kJ/V•mol)(0.123 V) = -23.7 kJ/mol.

This is the free-energy change for the oxidationreduction reaction when acetaldehyde, ethanol, NAD⁺, and NADH are all present at 1 M concentrations. If, instead, acetaldehyde and NADH were present at 1 M, but ethanol and NAD+ were present at 0.1 M, the value for ΔG would be calculated as follows. First, the values of E for both reductants are determined (Eqn 13-7):

Then ΔE is used to calculate ΔG (Eqn 13-8):

it is thus possible to calculate the free-energy change for any biological oxidation at any concentrations of the redox pairs.

In many organisms, the oxidation of glucose supplies energy for the production of ATP. For the complete oxidation of glucose:

C₆H₁₂O₆ + 6O₂ 6CO₂ + 6H₂O

ΔG°' is -2,840 kJ/mol. This is a much larger change in free energy than that occurring during ATP synthesis (50 to 60 kJ/mol; see Box 13-2). Cells do not convert glucose to CO₂ in a single, very energetic reaction, but rather in a series of reactions, some of which are oxidations. The free-energy change of these oxidation steps is larger than, but of the same order of magnitude as, that required for ATP synthesis from ADP. Electrons removed in these oxidation steps are transferred to coenzymes specialized for carrying electrons, such as NAD⁺ and FAD, which are described below.

Most cells have enzymes to catalyze the oxidation of hundreds of different compounds. These enzymes channel electrons from their substrates into a few types of universal electron carriers. The nucleotides NAD⁺, NADP⁺, FMN, and FAD are water-soluble cofactors that undergo reversible oxidation and reduction in many of the electron transfer reactions of metabolism. Their reduction in catabolic processes results in the conservation of free energy released by substrate oxidation. The nucleotides NAD⁺ and NADP⁺ move readily from one enzyme to another, but the flavin nucleotides FMN and FAD are very tightly bound to the enzymes, called flavoproteins, for which they serve as prosthetic groups. Lipid-soluble quinones such as ubiquinone and plastoquinone act in the nonaqueous environment of membranes, accepting electrons and conserving free energy. Iron-sulfur proteins and cytochromes are proteins with tightly bound prosthetic groups that undergo reversible oxidation and reduction; they, too, serve as electron carriers in many oxidation-reduction reactions. Some of these proteins are soluble, but others are peripheral or integral membrane proteins (p. 277). We will describe some chemical features of nucleotide cofactors and of certain enzymes (dehydrogenases and flavoproteins) that use them. The oxidation-reduction chemistry of quinones, iron-sulfur proteins, and cytochromes will be discussed in Chapter 18.